Analyze the provided image and identify any geometric figures or mathematical problems presented. Describe the figures and explain any visible mathematical concepts or tasks.

Image Analysis: Geometric Figures and Mathematical Tasks

The image displays a table (Таблица 11) with the title 'ПРИЗНАКИ РАВЕНСТВА ПРЯМОУГОЛЬНЫХ ТРЕУГОЛЬНИКОВ' (Criteria for Congruence of Right-Angled Triangles). It contains 10 numbered diagrams, each illustrating one or more right-angled triangles. The accompanying instruction is 'Найдите пары равных треугольников и докажите их равенство' (Find pairs of congruent triangles and prove their congruence).

Diagrams and Potential Tasks:

• Diagram 1: Shows two right-angled triangles, ABC and ADC, sharing a common side AC. There are markings indicating that angle B and angle D are right angles, and sides AB and AD are equal. This suggests a task to prove the congruence of triangles ABC and ADC using the hypotenuse-leg (HL) or side-angle-side (SAS) congruence postulates, depending on what other information can be inferred or is explicitly marked.
• Diagram 2: Depicts a triangle AKM with a line segment KT perpendicular to AM. K is a point on AM and T is a point on AM. There are markings indicating that angle AKM is a right angle and that segment AK is equal to segment KM. This is likely a task to analyze triangle AKM itself, perhaps to determine its type or properties.
• Diagram 3: Presents a triangle with vertices P, K, and R. Angle P and angle R appear to be acute, and angle K is divided into two smaller angles. There is a line segment from K perpendicular to PR, meeting PR at a point (let's assume it's T, though not labeled). There are markings indicating that angle PKT and angle RKT are equal, and that KT is perpendicular to PR. This setup suggests proving that triangle PKT is congruent to triangle RKT, likely using the Angle-Side-Angle (ASA) or Angle-Angle-Side (AAS) congruence postulates, leading to the conclusion that triangle PKR is isosceles.
• Diagram 4: Shows a quadrilateral with vertices R, B, E, S. Angles at R and S are right angles. There is a diagonal BE. This could be a task to prove the congruence of triangles RBE and SBE, likely using hypotenuse-leg (HL) if BE is shown as a common hypotenuse and RB=SB, or side-angle-side (SAS) if other conditions are met.
• Diagram 5: Presents a figure with vertices R, M, T, S, and a diagonal RT. Angles at P and M are marked as right angles. Segments RP and MS are marked as equal. This diagram is complex and could involve proving congruence of triangles RMP and TMS, or analyzing quadrilateral RMTS.
• Diagram 6: Shows two triangles ABC and ADC with a common side AC. Angles at E and P are right angles. Sides CE and CP are marked as equal. Sides AE and AP are marked as equal. This suggests proving congruence of triangles AEC and APC, likely using the SAS or SSS postulates.
• Diagram 7: Presents two triangles, MNT and MTR, sharing a common side MT. Angles at M and T are marked as right angles. Side MN is equal to side MR. This is a classic setup for proving congruence of right-angled triangles using the hypotenuse-leg (HL) postulate.
• Diagram 8: Shows two triangles, LRN and LMN, sharing a common side LN. Angles at R and M are marked as right angles. Side LR is equal to side LM. Similar to Diagram 7, this is for proving congruence using the HL postulate.
• Diagram 9: Depicts a quadrilateral with vertices C, B, E, A, and a diagonal CA. Angles at B and E are marked as right angles. Side CB is equal to side EA. This setup might involve proving congruence of triangles CBA and EAC using SAS or HL if AC is a common hypotenuse and AB=EC.
• Diagram 10: Shows two triangles, ADC and ABC, with a common side AC. Angles at D and B are marked as right angles. Side AD is equal to side AB. This is another example for proving congruence using the HL postulate.

The overall task is to apply the criteria for congruence of right-angled triangles, which typically include Hypotenuse-Leg (HL), Leg-Leg (LL), Angle-Leg (AL), or Angle-Angle-Side (AAS) if adapted for right triangles, to identify and prove congruent pairs among the given figures.